Variable LLR Scaling in Min-Sum Decoding for Irregular LDPC Codes

Min-sum decoding is a low-complexity alternative to the so-called belief propagation and consists in simplification of the nonlinear operation on the log likelihood ratios (LLRs) in the check nodes. The resulting suboptimality may be tempered via appropriate scaling of the LLRs, e.g., the fixed optimal scaling in the normalized min-sum algorithm, and variable scaling algorithms gradually appearing in the literature. However, up to now, none of the papers studied variable scaling both as per iteration and as per different check node degree, due to the prohibitive complexity of multioptimization over space of too many parameters. In this paper, we propose a generalized mutual information (GMI) of LLRs as the criterion to search for the scaling factors for different check node degrees in every iteration in a 1-D thus low-complexity manner. This approach is first analyzed via density evolution, and in addition can be extended to practical LLRs based formulas via Monte Carlo tools to cope with the mismatch issue. Bit error rate simulation results on two low-density parity-check codes show that our proposed GMI metrics have a noticeable gain over the variable scaling schemes that appeared in the literature.